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© K.Cuthbertson and D.Nitzsche LECTURE RISK GRADES™ : J.P Morgan Version 1/9/2001
© K.Cuthbertson and D.Nitzsche Data on Returns and Volatility RiskGrades™ (J.P. Morgan) Risk Grades for Various Portfolios Topics
© K.Cuthbertson and D.Nitzsche Data on Returns and Volatility
© K.Cuthbertson and D.Nitzsche HOW RISKY ARE STOCKS? US - STOCK RETURNS: LONG TERM (1929-54) June 22nd, 1929$10,000 Sept 3rd, 1929$12,417 (+25%) Oct 29th, 1929$ 7,495 July 1932$ 1,342 (-86%) 1954$10,000
© K.Cuthbertson and D.Nitzsche Jan 1973$10,000 Dec 1974$ 6,600 (-34%) 1983$10,000 US - STOCK RETURNS: LONG TERM (1973-83)
© K.Cuthbertson and D.Nitzsche Jan 1988$10,000 Dec 1989$18,342 July 1992$ 6,708 (-33%) Jan 2000<$10,000 JAPAN - STOCK RETURNS: (1988-2000)
© K.Cuthbertson and D.Nitzsche MeanS.D. Large US stocks1.0295.7%(per month) Normality Only 1% of the time should monthly stock return fall below 1.029 - 2.33(5.7%) = -12.25% 1929-97 = 828 months How many returns more negative than -12.25%? Normality = 8.3Actual = 16 ! Never, trust the ‘normal’ ! US STOCKS: SHORT TERM (Monthly 1926-97)
© K.Cuthbertson and D.Nitzsche RiskGrades™ (J.P. Morgan)
© K.Cuthbertson and D.Nitzsche A ‘simplified’ method of calculating the changing risk (usually daily) of a portfolio of assets, for use by individual investors and ‘small’ financial institutions. Measures change in risk in a transparent and simple way The returns on the portfolio are ignored (in large part) Concepts based on elementary portfolio theory RiskGrades measures volatility ( ) as the S.D. of a portfolio of assets. is usually measured as an EWMA of past squared (daily) returns ( r t = ln(P t /P t-1 ) ) - using = 0.97 and about 150 days/values for r t RiskGrades™ : What is it ?
© K.Cuthbertson and D.Nitzsche 1) “Portfolio Risk Grade” Risk of portfolio (relative to 20% risk of a ‘world’ benchmark) 2) Undiversified Risk Grade ~ worse case outcome 3) Diversification Benefit = (2) - (1) 4) Marginal Risk Impact = increase in risk as you add (or subtract) one or more assets from your portfolio Statistics Used
© K.Cuthbertson and D.Nitzsche i is the DAILY standard deviation base is fixed at 20% per annum(=av. for international stocks) Hence RG is just a “scaled” standard deviation e.g. If RG = 100% then asset has 20% p.a. ‘absolute’ risk e.g. If RG 1 = 100 and RG 2 = 400 then asset-2 currently has 4 times the risk of asset-1 RiskGrades™ (single asset)
© K.Cuthbertson and D.Nitzsche VCV = variance-covariance matrix of RG Undiversified Risk Grade(Worse case) Undiversified RG = all w>0 Diversification Benefit = URG - RG RISK GRADE (Portfolio)
© K.Cuthbertson and D.Nitzsche $RI = RG p (n) - RG p (n-j) = risk grade whole portfolio – risk grade excluding one (or more) assets Funds released are held in cash (zero risk/correlation) %Percent Risk Impact of omitted asset – j % RI = Can RI ever increase as you ‘drop’ an asset ? $ RISK IMPACT of omitted asset (= j)
© K.Cuthbertson and D.Nitzsche RiskGrades™: FT 19/10/00 (for Oct 17th) BONDSEQUITYFX(rel to USD) Europe2586(135)62(Euro) Americas3294(146)49 Asia2198(139)39(Yen) Global38107(156)…. UK77 (115) Note: (..) = 52-week high 100 = average volatility of international equity mkts (equiv, to 20% p.a. absolute volatility).
© K.Cuthbertson and D.Nitzsche An Example ($10,000 in each of 2 assets) WeightsRisk Grade%R.I. Coca-Cola½18828 Cisco½17925 Portfolio125 Diversification58.5 The Risk Grade for various stock indices are now published daily in the Financial Times. Risk Measures
© K.Cuthbertson and D.Nitzsche 1) Cola’s RG is ‘9’ more than Cisco’s RG - what does this mean? 2) What is the ‘Undiversified RG’ and the ‘Diversification (RG) effect ? Class Exercise: Interpretation of the Figures
© K.Cuthbertson and D.Nitzsche 3)How do we get the figure of 28% for the Percentage Risk Impact of Cola and what does this 28% mean? Hint: Note that when you remove Cola, then these funds are held in cash(with zero risk) and you continue to hold only Cisco. Class Exercise: ‘Risk Impact and %R.I.’
© K.Cuthbertson and D.Nitzsche P t = DPV (y t C, M, n) Use historic(daily) y t to calculate ‘simulated’ P t. (n, C and M are ‘fixed’ by the bond you hold) Capital gain = ln(P t /P t-1 ) “Return” = CG + y t /252 Calculate S.D. of ‘Return’(I.e EWMA using 150 days past data) Illustrative RG for Government Bonds (different maturities) RG (¼, ½, 1, 10, 30yr) = 1, 2, 3, 26, 43 respectively What does RG=43 for 30 year bond mean? What is it so much larger than RG=3 for 1-yr bond? RiskGrades for Bonds
© K.Cuthbertson and D.Nitzsche Black-Scholes Formula C t = BS(S t, r t, , T, Div) Use historic values of 1 st, 2 variables. Construct artificial data series for C t (with , T, Div fixed): “Return” = ln(C t /C t+1 ) Calculate S.D. of Return Are there any dangers in this method ? Can it be applied to all options ? Risk Grade for Bonds
© K.Cuthbertson and D.Nitzsche Risk Grades for Various Portfolios
© K.Cuthbertson and D.Nitzsche Price/ValueR. GradeR. Impact % Cisco107.12517971 Call18.12566529 Div.Ben22 Portfolio125.25227 What is the ‘undiversified RG’ and why is the ‘Div Benefit’ rather low at ‘22’? Intuitively, why is the RG of the call relatively high at ‘665’? (Hint: assume it’s ‘delta’ is say 0.5) - tricky! Portfolio = 1 share Cisco +1 At-the-money call on Cisco
© K.Cuthbertson and D.Nitzsche PriceR. Grade %R. Impact Cisco107.12517941 Put11.75600-58 Div. Ben119 Portfolio118.875102 Why is the diversification benefit relatively high at 199 Intuitively what does a %R.I of -58 mean? Portfolio = 1 share Cisco + 1 At-the-money Put
© K.Cuthbertson and D.Nitzsche a) $10,000 in Cola - all own funds b) $10,000 in Cola, $5000 borrowed funds(ignore interest cost) a)$’sRisk Grade%R.I. Cola10,000188 100 Cash00 : Div. Benefit0: : ‘Portfolio’10,000188 : b)$’sRisk Grade%R.I. Cola10,000188 100 Cash-5,0000 0 Div. Benefit:0 : ‘Portfolio’5,000376 : Intuitively, why has RG of ‘portfolio’ increased to 376. Is there an obvious formula in this simple case? RiskGrades with purchases ‘on margin’(=Leverage)
© K.Cuthbertson and D.Nitzsche Intuitively, why is RG=376 relatively high? Intuitively, why is there a ‘R.I.’ for ‘cash’ whereas there was no such effect for purchases ‘on margin’ ? RiskGrades with purchases financed from ‘short sales’
© K.Cuthbertson and D.Nitzsche a) $10,000 in Cola - all own funds b) $10,000 in Cola using $5000 funds obtained from short selling Cisco (ignore any ‘haircuts’) a)$’sRisk Grade%R.I. Cola10,000188 100 Cash0: : Div. Benefit0: : ‘Portfolio’10,000188 : b)$’sRisk Grade%R.I. Cola10,000188 58 Cash-5,000179 12 Div. Benefit:127 : ‘Portfolio’5,000376 : RiskGrades: purchases financed from ‘short sales’
© K.Cuthbertson and D.Nitzsche END OF LECTURE
© K.Cuthbertson and D.Nitzsche 1) RG (Cola) – RG(Cisco) = 188-179 = 9 [i.e. Cola is 1.8%p.a. (= 9 x 20%/100) more volatile than Cisco in absolute terms]. 2) Undiversified RG = (½)(188)+(½)179 = 183.5 Hence: Diversification effect= 183.5-125 = 58.5 3)Risk Impact of Cola(extreme case of only 2 assets) %RI(Cola)= Note that ‘179’ is Cisco’s risk grade. Note (½) in Cisco and ½ is held in cash (with zero risk). Interpretation of Figures (see above slides)
© K.Cuthbertson and D.Nitzsche Removing Cola from the portfolio would reduce RG by 35.5 which is equivalent to 7% of the annual S.D. (= 35.5 x 0.20) Removing Cola from the portfolio would reduce the risk grade in percentage terms by 28% (I.e. compared with the RG of the initial 2-asset portfolio) This 28% reduction in risk is primarily due to the fact that in the initial 2-asset portfolio you hold 2 x $10,000 in risky assets while after removing Cola you only hold $10,000 in risky assets (The other $10,000 is held in cash). Interpretation of ‘Risk Impact’
© K.Cuthbertson and D.Nitzsche END OF SLIDES
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